Answer:

And we can set equal this derivate to 0 in order to find the critical point and we got:


And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094
Step-by-step explanation:
For this case we have the following function:

Where P represent the annual net income for the period 2007-2011 and 
And t represent the time in years since the start of 2005
In order to find the lowet income we need to use the derivate, given by:

And we can set equal this derivate to 0 in order to find the critical point and we got:


And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094
2 students play on the softball team
<u>Solution:</u>
Given that in a class of 25 students, 8 % of students play on a softball team
To find: Number of students play on softball team
Total number of students in class = 25
8 % of students play on a softball team means that 8 % of total students play on softball team
Therefore, number of students play on softball team is given as:

Thus 2 students play on the softball team
Answer:
y=2x+10
Step-by-step explanation:
In line equations its helpful to write your line in the form y = ax + b. This helps because a is always the gadient of the line and b is always the y intercept.
In this case it is y=2x+3
All parallel lines have the same gradient. The gradient of this line = 2.
If the line crosses the x axis at x=-5, then when x =-5 y = 0.
If you put all this in the form y =ax + b you get 0 = 2(-5) +b
So all you need to do to find b is rearrange. b = 10.
Therefore your line has gradient 2 and y intercept 10.
y = 2x + 10
Answer:
0.0008
Step-by-step explanation:
The formula for a hypergeometric probability is

where N is the population, A is the number of objects of type A, B is the number of objects of type B, n is the sample size and x is the number of successes.
In this problem, N is 13. A is 5, since there are 5 objects drawn, and B is 8, since there are 8 remaining objects.
The sample size, n, is 5, and x is 5:

Step-by-step explanation:
5x+8-3x=-10
2x+8= -10
2x=-10-8
2x=-18
therefore x= -9